Biomedical Engineering Reference
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spectively. It is well known that regular-spiking neurons support extremely low fre-
quency regular firing [10], which is class 1 behaviour. Erisir et al. [14] describe how
FS neurons begin repetitive firing “with abrupt onset” for increasing levels of steady
stimulus current. We have also observed that fast-spiking neurons have an abrupt
onset of regular firing, and when held near the threshold switch between episodes of
quite high frequency firing and subthreshold oscillations at a similar frequency (inset
of
Figure 6.10
[48]). This is typical class 2 behaviour.
To better illustrate the difference between dynamical classes, we examined delay
representations [33, 43] of near-threshold responses to steady current injection in RS
and FS cells. There is no added noise, only intrinsic noise, essentially ion channel
gating noise. Three-dimensional representations are shown in Figure 6.10. Trajec-
tories in this space did not reproducibly self-intersect, suggesting that even with this
small number of time delay dimensions, there is a 1:1 transformation of the motion of
the principal underlying dynamical variables [62]. Using lags of 1 and 10 ms to un-
fold movement at fast and slow timescales, FS neurons (Figure 6.10A) showed two
patterns of perturbation - uniform perturbation of the spike loop (horizontal limb)
and noisy resonant loops (inset) in a basin from which there are intermittent escapes
to spike. In RS neurons (Figure 6.10B), uniform perturbation of the spiking loop is
also seen, but as for the class 1 model, subthreshold movement lacks fast oscillation
structure, and is a very slow drift of random movement (inset). Thus, variability of
firing in two major types of cortical neurons, RS and FS, also appear to follow the
qualitative patterns shown by class 1 and class 2 models, respectively.
6.10
Implications for synchronous firing
The explosion of variability in the late stage must be partly responsible for breaking
up transient synchrony of firing in the local cortical network. As soon as adaptation,
inactivation and synaptic depression bring the level of firing down to a critical point,
the entry of many cells into the late stage would destroy the
coherence
of firing
which is itself essential for maintaining the high level of input to each cell during
the transient. Pyramidal RS cells appear to associate inputs from different layers
and areas in the cortex, via the back-propagation activated dendritic calcium spike
mechanism [37]. Class I dynamics of RS neurons, with its early entry into the late
stage, might allow relatively easy
switching
between different tempos in their inputs.
It may also promote the generally high level of firing variability in the cortex [25] -
probably over 50% of cortical cells are class 1 RS neurons.
On the other hand, class 2 FS neurons, which inhibit each other and other RS
neurons locally, are implicated in promoting synchronous firing [6, 20]. They are
coupled together by electrical synapses or gap junctions, which helps to synchronise
their action potentials precisely. The nature of class 2 dynamics may mean that the
phase of rhythmic firing is quite stable even when the mean stimulus goes subthresh-
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